I see you are recently familiar with Z))) It is advised to treat the surface with a protective agent after cleaning - it prevents dust from adhering, and also protects against cracking of leather and plastic. I used on my Z 303 Automotive Protectant but you can try something else. I chose here Best car interior dressing | Interior dressing for auto detailing also this manual describes what is interior dressing car and how best to produce it .
Wash with a WOOL mitt, use a wax-based car shampoo, not dish soap. Dawn will cut all the wax off the paint.
Best drying chamois are those yellow synthetic ones from Germany - $20 for a pack of four. You can cut one in half it it's too large. Can get them here:
Armorall is an inferior product - try 303 Aerospace protectant instead. "40SPF for your stuff". Good for all rubber, vinyl, and plastic surfaces. Non-oily, non-shiny, deep color. Comes from the marine and aircraft industries. You'll thank me later.
And my favorite glass cleaner, tint or no, is Sprayaway. Can get it at any big-box store, wallyfart, HD, etc. Low-lint paper towel works great - my favorite is Brawny. Most other brands are inferior and leave a lot of paper lint.